a(b(

R

↳Dependency Pair Analysis

A(b(x)) -> A(a(x))

A(b(x)) -> A(x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Narrowing Transformation

**A(b( x)) -> A(x)**

a(b(x)) -> b(b(a(a(x))))

innermost

On this DP problem, a Narrowing SCC transformation can be performed.

As a result of transforming the rule

one new Dependency Pair is created:

A(b(x)) -> A(a(x))

A(b(b(x''))) -> A(b(b(a(a(x'')))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Forward Instantiation Transformation

**A(b(b( x''))) -> A(b(b(a(a(x'')))))**

a(b(x)) -> b(b(a(a(x))))

innermost

On this DP problem, a Forward Instantiation SCC transformation can be performed.

As a result of transforming the rule

two new Dependency Pairs are created:

A(b(x)) -> A(x)

A(b(b(x''))) -> A(b(x''))

A(b(b(b(x'''')))) -> A(b(b(x'''')))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳FwdInst

...

→DP Problem 3

↳Forward Instantiation Transformation

**A(b(b(b( x'''')))) -> A(b(b(x'''')))**

a(b(x)) -> b(b(a(a(x))))

innermost

On this DP problem, a Forward Instantiation SCC transformation can be performed.

As a result of transforming the rule

two new Dependency Pairs are created:

A(b(b(x''))) -> A(b(x''))

A(b(b(b(x'''')))) -> A(b(b(x'''')))

A(b(b(b(b(x''''''))))) -> A(b(b(b(x''''''))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳FwdInst

...

→DP Problem 4

↳Remaining Obligation(s)

The following remains to be proven:

**A(b(b(b(b( x''''''))))) -> A(b(b(b(x''''''))))**

a(b(x)) -> b(b(a(a(x))))

innermost

Duration:

0:00 minutes